You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block. The spring's maximum compression d is measured from its initial suspended position. a. Find an expression for the bullet's initial speed vB in terms of m, M, k, and d. What quantity is conserved in an inelastic collision? Subsequently the block hits a spring on a frictionless surface. What quantity is conserved in this collision? b. What was the speed of a 5.0 g bullet if the block's mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 10 cm? c. What fraction of the bullet's initial kinetic energy is "lost"? Where did it go?